Problem: It is currently $3\!:\!00\!:\!00 \text{ p.m.}$ What time will it be in $6666$ seconds?  (Enter the time in the format "HH:MM:SS", without including "am" or "pm".)
Explanation: There are $60$ seconds in a minute. When $6666$ is divided by $60$, you get $111$ with a remainder of $6$ seconds. Therefore, $6666$ seconds is $111$ minutes and $6$ seconds. There are $60$ minutes in an hour. When you divide $111$ by $60$, you get $1$ with a remainder of $51$. Thus, $6666$ seconds is equivalent to $1$ hour $51$ minutes and $6$ seconds. Therefore, the time in $6666$ seconds is $\boxed{4\!:\!51\!:\!06 \text{ p.m.}}$